Polynomial Expansion Using Pascals Triangle

**nugiboy** · May 3rd 2008, 08:24 AM

Heres the question followed by the textbook answer from the back.

Im stuck on how it got the answer. Ive just done about 5 others in the same way, but this one doesn't seem to give me the right answer.

I got:

$1+12x+30x^2+40x^3+30x^4+12x^5+2x^6$

I did the correct method i think.
Heres the row of the pascal triangle i used:

1 6 15 20 15 6 1

So i basicly did:

$(1)(1^6)(2x^0) + (6)(1^5)(2x^1) + (15)(1^4)(2x^2)$ ... etc and simplified. I really don't understand how i got the answer wrong. Any suggestions?

**Moo** · May 3rd 2008, 08:28 AM

Hello,

Originally Posted by nugiboy

Heres the question followed by the textbook answer from the back.

Im stuck on how it got the answer. Ive just done about 5 others in the same way, but this one doesn't seem to give me the right answer.

I got:

$1+12x+30x^2+40x^3+30x^4+12x^5+2x^6$

I did the correct method i think.
Heres the row of the pascal triangle i used:

1 6 15 20 15 6 1

So i basicly did:

$(1)(1^6)({\color{red}(}2x{\color{red})}^0) + (6)(1^5)({\color{red}(}2x{\color{red})}^1) + (15)(1^4)({\color{red}(}2x{\color{red})}^2)$ ... etc and simplified. I really don't understand how i got the answer wrong. Any suggestions?

The mistakes are in red

**james_bond** · May 3rd 2008, 08:29 AM

Remember that it is $\left(1+\left(2x\right)\right)^6$ !

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